BT007Y

beta_repeat_transport_entry

Stable checked-use theorem · independently kernel verified

Repeat prefixes with one value preserve every decoded entry extensionally.

Current library: Alpha v34, 4,223 checked-use theorems; Stable remains 432. Historical first admissions, original proof editions, and non-admitted aliases are preserved. Exact original first-admission records.

Exact expanded PA statement

forall b c z d a l. (forall ff_i_transport_l. (exists ff_lt_transport_l_bound. ff_lt_transport_l_bound + S ff_i_transport_l = l) -> (((exists ff_h_transport_l_decoded. ff_h_transport_l_decoded + S (a) = S ((S (ff_i_transport_l)) * c)) /\ exists ff_q_transport_l_decoded. b = ff_q_transport_l_decoded * S ((S (ff_i_transport_l)) * c) + (a)))) -> (forall ff_i_transport_r. (exists ff_lt_transport_r_bound. ff_lt_transport_r_bound + S ff_i_transport_r = l) -> (((exists ff_h_transport_r_decoded. ff_h_transport_r_decoded + S (a) = S ((S (ff_i_transport_r)) * d)) /\ exists ff_q_transport_r_decoded. z = ff_q_transport_r_decoded * S ((S (ff_i_transport_r)) * d) + (a)))) -> forall i x. (exists h. h + S i = l) -> (((exists ff_h_transport_x. ff_h_transport_x + S (x) = S ((S (i)) * c)) /\ exists ff_q_transport_x. b = ff_q_transport_x * S ((S (i)) * c) + (x))) -> (((exists ff_h_transport_y. ff_h_transport_y + S (x) = S ((S (i)) * d)) /\ exists ff_q_transport_y. z = ff_q_transport_y * S ((S (i)) * d) + (x)))

Structural proof guide

Repeat prefixes with one value preserve every decoded entry extensionally.

Direct prerequisites: beta_repeat_entry_eq. The authored body proceeds by intermediate claims (1), equality transport (2).

Proof neighborhood

Direct dependencies

BT007X beta_repeat_entry_eq

Direct dependents

BT0082 pow_functional

Formal native tactic body

Dependencies are hypotheses of the historical Alpha-v12 body receipt. The complete historical Alpha-v18 proof bundle independently checks every dependency; current Alpha v25 preserves that checked theorem use without changing Stable membership.

Read the argument

Proof checkpoints

28 script commands · 6 reading checkpoints · 1 local claims

This is a reading aid, not a new proof or a proof-tree certificate. Checkpoint groups are consecutive commands, not inferred branch boundaries. Every step links to the preserved script.

Named ingredients (1)
beta repeat entry eq
01Fix variables and assumptionsL1–10

Work with arbitrary variables or the premises of the current implication.

  1. L1
    intro b
  2. L2
    intro c
  3. L3
    intro z
  4. L4
    intro d
  5. L5
    intro a
  6. L6
    intro l
  7. L7
    intro hleft
  8. L8
    intro hright
  9. L9
    intro i
  10. L10
    intro x
02Fix variables and assumptionsL11–12

Work with arbitrary variables or the premises of the current implication.

  1. L11
    intro hi
  2. L12
    intro hx
03Establish hxaL13–22

Establish this local claim before using it. It is not an additional assumption. The following proof commands apply beta repeat entry eq.

  1. L13
    have hxa : x = a
  2. L14
    specialize beta_repeat_entry_eq b
  3. L15
    specialize beta_repeat_entry_eq c
  4. L16
    specialize beta_repeat_entry_eq a
  5. L17
    specialize beta_repeat_entry_eq l
  6. L18
    specialize beta_repeat_entry_eq i
  7. L19
    specialize beta_repeat_entry_eq x
  8. L20
    apply beta_repeat_entry_eq
  9. L21
    exact hleft
  10. L22
    exact hi
04Use earlier factsL23–23

Instantiate or apply named facts and discharge the corresponding proof obligations.

  1. L23
    exact hx
05Calculate and transport equalitiesL24–25

Carry out the recorded arithmetic or equality steps; inspect the exact commands for their direction and premises.

  1. L24
    rewrite hxa
  2. L25
    rewrite hxa
06Use earlier factsL26–28

Instantiate or apply named facts and discharge the corresponding proof obligations.

  1. L26
    specialize hright i
  2. L27
    apply hright
  3. L28
    exact hi

Library-wide reading audit

Original exact command ledger · 28 lines
  1. 0001intro b
  2. 0002intro c
  3. 0003intro z
  4. 0004intro d
  5. 0005intro a
  6. 0006intro l
  7. 0007intro hleft
  8. 0008intro hright
  9. 0009intro i
  10. 0010intro x
  11. 0011intro hi
  12. 0012intro hx
  13. 0013have hxa : x = a
  14. 0014specialize beta_repeat_entry_eq b
  15. 0015specialize beta_repeat_entry_eq c
  16. 0016specialize beta_repeat_entry_eq a
  17. 0017specialize beta_repeat_entry_eq l
  18. 0018specialize beta_repeat_entry_eq i
  19. 0019specialize beta_repeat_entry_eq x
  20. 0020apply beta_repeat_entry_eq
  21. 0021exact hleft
  22. 0022exact hi
  23. 0023exact hx
  24. 0024rewrite hxa
  25. 0025rewrite hxa
  26. 0026specialize hright i
  27. 0027apply hright
  28. 0028exact hi